Cube corner reflectors are well-known optical elements that are used in a variety of optical systems. A cube corner reflector 100 as illustrated in FIG. 1 has three planar reflective surfaces 110, 120, and 130 that intersect at right angles in the same manner as the intersection of faces at the corner of a cube. Reflective surfaces 110, 120, and 130 can be formed on three sides of a tetrahedral glass block that also has a transparent face 140 for input of an incident beam and output of a reflected beam. The tetrahedral glass block in cube corner reflector 100 is symmetric so that the perimeter of transparent face 140 forms an equilateral triangle and the perimeters of reflective surfaces 110, 120, and 130 are congruent isosceles right triangles.
Cube-corner reflector 100 is a retroreflector, and therefore a reflected beam from cube-corner reflector 100 is parallel to but offset from an incident beam regardless of the direction of the incident beam. FIG. 1 illustrates an example of an incident beam 180 that enters cube corner reflector 100 through transparent face 140 and reflects from one or more of reflective faces 110, 120, and 130 before exiting as a reflected beam 190. Reflected beam 190 is parallel to incident beam 180 and offset from incident beam 180 by twice the perpendicular separation between incident beam 180 and a vertex 150 of cube corner reflector 100.
The tetrahedral shape of cube corner reflector 100 includes more glass than is generally required for the optical function of cube corner reflector 100, particularly in optical systems where the location and direction of the incident beam is well controlled. Cube corner reflector 100 can thus be trimmed to remove glass that is not required for the optical function of cube corner reflector 100. One conventional way to trim cube corner reflector 100 is to take a cylindrical core of cube corner reflector 100, which results in transparent face 140 having a circular perimeter. Another known trimming scheme gives transparent face 140 a rectangular boundary 145.
FIG. 2 shows a cube corner reflector 200 resulting from trimming cube corner 100 at boundary 145. Cube corner reflector 200 is small for a retroreflector capable of reflecting an incident beam 280 to provide an offset reflected beam 290. The minimum required size of cube corner reflector 200 to perform this optical function depends on the desired offset between incident and reflected beams 280 and 290, the diameters or areas of beams 180 and 290, and the path of the beams inside cube corner reflector 200. To minimize the area of the face of cube corner reflector 200, incident beam 280 (or alternatively reflected beam 290) is centered at a point on an edge 235 of cube corner reflector 200.
Analysis of the beam paths in cube corner reflector 200 shows the if incident beam 280 is parallel to a central axis of cube corner reflector 200 then the beam paths will remain within a band having boundaries at the upper and lower edges of beams 280 and 290 in FIG. 2. For example, a ray 282 at a top edge of incident beam 280 reflects from a reflective face 210 toward a reflective face 230 and then reflects from a point on reflective face 230 that is at the same height as the bottom edge of incident beam 280. From there, the ray travels horizontally to reflective surface 220 and exits as a reflected ray 292 at the bottom of reflected beam 290. Similarly, a ray 284 at the bottom of incident beam 280 reflects from reflective surface 230 to a point on reflective surface 210 at the same height as the top of incident beam 280, travels horizontally to the top of reflected beam 290, and exits as reflected ray 294. The height of cube corner reflector 200 can thus be as small as the diameter of beams 280 and 290 plus an added margin for beam variations or misalignments.
FIG. 3 illustrates a known multi-axis plane mirror interferometer 300 employing four cube corner reflectors 200. U.S. Pat. No. 09/876,531, entitled xe2x80x9cMulti-Axis Interferometer With Integrated Optical Structure And Method For Manufacturing Rhomboid Assembliesxe2x80x9d further describes some examples of multi-axis interferometers containing retroreflectors that can be implemented using cube corner reflectors.
Interferometer 300 has four input beams IN1 to IN4 that are direction into a polarizing beam splitter 310. Polarizing beam splitter 310 splits input beams IN1 to IN4 into components according to polarization. Components of one polarization from input beams IN1 to IN4 become respective measurement beams M1 to M4, and components of an orthogonal polarization in input beams IN1 to IN4 become reference beams (not shown). Measurement beams M1 to M4 travel from polarizing beam splitter 310 to a planar measurement reflector (not shown) that is mounted on an object being measured. The measurement reflector returns measurement beams M1 to M4 along the same paths.
Polarization changing elements (e.g., quarter-wave plates) 320 are in the paths of outgoing and returning measurement beams M1 to M4 and change the polarization of measurement beams M1 to M4 so that polarization beam splitter 310 directs the returning measurement beams M1 to M4 to respective cube corner reflectors 200.
Cube corner reflectors 200 reflect returning measurement beams M1 to M4 so that offset measurement beam M1xe2x80x2 to M4xe2x80x2 can traverse polarizing beam splitter 310 and elements 320, reflect from the measurement reflector, and return through elements 320 and polarizing beam splitter 310 to form parts of respective output beams OUT1 to OUT4. Each measurement axis of interferometer 300 corresponds to a pair of beams M1 to M1xe2x80x2, M2 and M2xe2x80x2, M3 and M3xe2x80x2, or M4 and M4xe2x80x2 and to a measured point that is halfway between the centers of the incident areas of the corresponding pair on the measurement mirror. Accordingly, cube corner reflectors 200 must be small enough to fit within the spacing of measurement beams M1 to M4 and M1xe2x80x2 to M4xe2x80x2 that is required for the desired measurement axes.
The reference beams have paths that include first reflections from a reference reflector (not shown), reflections from respective cube corner reflectors 200, and second reflections from the reference reflector before the reference beams rejoin respective measurement beams M1xe2x80x2 to M4xe2x80x2 in output beams OUT1 to OUT4. The two reflections of each measurement beam from the measurement reflector, the two reflections of each reference beam from the reference reflector, and the intervening reflections from the associated cube corner reflector 200 are well known to eliminate an angular separation that misalignment of the measurement or reference mirror might otherwise cause between the reference and measurement beams in the combined output beam.
A measurement along a measurement axis of interferometer 300 requires measuring and analyzing the phases of the measurement and reference beams that are within the output beam associated with the measurement axis. These measurements are most accurate if the wavefronts of measurement and reference beams are uniform because the measured phase information is generally an integral or average of the phase information over a cross-section of the output beam. Further, the integrated/analyzed portion of the measurement beam typically changes because of beam xe2x80x9cwalk-offxe2x80x9d. Beam walk-off occurs when the object being measured changes angular orientation. The walk-off changes the matched portions of the measurement and reference beams, causing an erroneous phase shift when the beam wavefront is nonuniform. Wavefront distortion can thus cause errors and lower signal-to-noise ratios in phase information measurements and correspondingly in the measurements along the measurement axes of interferometer 300.
Returning to FIG. 2, edge 235 of cube corner reflector 200 passes through the center of incident beam 280. The reflection of a beam from edge 235 is generally nonuniform and distorts the wavefront of the reflected beam. Such non-uniformity may arise from a chamber formed to improve the safety or durability of an otherwise sharp edge and from roll off that commonly arises at the edges of polished optical surfaces. This wavefront distortion can be significant for an interferometer measurement particularly because wavefront distortion from the edge crosses through the center of the beam where light intensity is high.
Another source of wavefront distortion in cube corner reflector 200 arises from reflective surfaces 210, 220, and 230 not being perfectly orthogonal. When incident beam 280 is incident on edge 235, the angular errors in the orientations of reflective surfaces 210, 220, and 230 cause the wavefront (i.e., the surface of uniform phase) of output beam 290 to be V-shaped. This V-shape produces measurement errors when measuring a phase for a planar cross-section of the beam. Correcting for this type of wavefront distortion is difficult because expected beam movement relative to edge 235 typically changes which side of the V-shaped wavefront corresponds to the larger portion of beam intensity.
In view of the limitations of current cube corner reflectors, methods and structures that reduce the wavefront distortion caused in reflections from cube corner reflectors could improve measurement signal strength and the accuracy of interferometer measurements.
In accordance with an aspect of the invention, a cube corner reflector is oriented so that incident and reflected beams either entirely miss the edges at the intersections of reflective surfaces or so that the beams have only peripheral portions incident on the edges. The edges thus cause less wavefront distortion that could affect measurements in systems such as interferometers. With one such orientation, a symmetry plane that is midway between the incident and reflected beams of the cube corner reflector contains one of the edges of the reflective surfaces and a central axis that passes through the vertex of the cube corner reflector. A cube corner reflector having trimmed surfaces perpendicular to its symmetry plane can be closely spaced with other cube corner reflectors to provide a tight beam pattern in a multi-beam device. For minimum size, the trimmed surfaces that are perpendicular to the symmetry plane are at different distances from the central axis.
One specific embodiment of the invention is an optical element such as a cube corner reflector. The optical element has three orthogonal reflective surfaces with three edges at the intersections of the reflective surfaces. A first edge is at an intersection of the first reflective surface and the second reflective surface and is symmetrically located between an incident beam and a reflected beam of the optical element. A second edge is at an intersection of the second reflective surface and the third reflective surface, and a third edge is at an intersection of the third reflective surface and the first reflective surface. A first trimmed surface is parallel to a central plane that contains central rays of the incident and reflected beam.
The optical element may further have a second trimmed surface that is parallel to the first trimmed surface, but the parallel trimmed surfaces are asymmetrically located relative to the central axis through the vertex of the optical element. A perpendicular distance between the first trimmed surface and the central plane differs from a perpendicular distance between the second trimmed surface and the central plane. More specifically, a perpendicular distance between one trimmed surface and the central plane may be required to extend beyond a radius of the incident and reflected beam by at least a distance corresponding to a non-zero deflection of incident beam toward the trimmed surface in the optical element. The beam is deflected away from the other trimmed surface in the optical element so that the distance between that trimmed surface and the central plane can be about equal to the radius of the beams.
Another specific embodiment of the invention is a cube corner reflector. The cube corner reflector includes first, second, and third reflective surfaces, an input/output face, and at least one trimmed surface. The input/output face is perpendicular to a central axis through the vertex of the cube corner reflector and includes a first transparent aperture for an incident beam and a second transparent aperture for a reflected beam. One trimmed face intersects a first edge that is between the first and second reflective surfaces, with the first edge being in a plane that also includes the central axis of the cube corner reflector and passes midway between the first and second apertures.
A second trimmed surface is parallel to the first trimmed surface and is such that a second edge that is between the second and third reflective surfaces makes an angle with the second trimmed surface that is equal to the angle made with the second trimmed surface by a third edge that is between the third and first reflective surfaces. A perpendicular distance between the first trimmed surface and the central axis of the cube corner reflector can be less than a perpendicular distance between the second trimmed surface and the central axis of the cube corner reflector.